Data commit

Task/Pell-numbers/Haskell/pell-numbers.hs

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+import Data.Numbers.Primes (isPrime)
+
+----------------------- PELL SERIES ----------------------
+
+pell :: Integer -> Integer -> [Integer]
+pell a b = a : b : zipWith (+) (pell a b) ((2 *) <$> tail (pell a b))
+
+a000129, a002203, a001333, a086383, a096650, a002315 :: [Integer]
+a000129 = pell 0 1
+
+a002203 = pell 2 2
+
+a001333 = (`div` 2) <$> a002203
+
+a086383 = filter isPrime a000129
+
+a096650 = zip [0 ..] a000129 >>= (\(i, n) -> [i | isPrime n])
+
+a002315 = 1 : 7 : zipWith (-) ((6 *) <$> tail a002315) a002315
+
+
+------------------- PYTHAGOREAN TRIPLES ------------------
+
+pythagoreanTriples :: [(Integer, Integer, Integer)]
+pythagoreanTriples =
+  (tail . concat) $ zipWith3 go [0 ..] a000129 (scanl (+) 0 a000129)
+  where
+    go i p m
+      | odd i = [(m, succ m, p)]
+      | otherwise = []
+
+-------------------------- TESTS -------------------------
+main :: IO ()
+main = do
+  mapM_
+    (\(k, xs) -> putStrLn ('\n' : k) >> print (take 10 xs))
+    [ ("a000129", a000129)
+    , ("a002203", a002203)
+    , ("a001333", a001333)
+      -- Waste of electrical power ?
+      -- ("a086383", a086383)
+      -- ("a096650", a096650
+    , ("a002315", a002315)
+    ]
+
+  putStrLn "\nRational approximations to sqrt 2:"
+  mapM_ putStrLn $
+    (take 10 . tail) $
+    zipWith
+      (\n d ->
+         show n <>
+         ('/' : show d) <> " -> " <> show (fromIntegral n / fromIntegral d))
+      a001333
+      a000129
+
+  putStrLn "\nPythagorean triples:"
+  mapM_ print $ take 10 pythagoreanTriples